Theoretical sampling distributions, their practical limitations and some experimental results

Most of the important theoretical sampling distributions are based upon the assumption that the parent population is normal and the variates are independently distributed. In practice these requirements are never entirely realized, and in many instances, conditions may be radically different from those assumed by the theory. The questions which naturally follow are: Is this theory still valid in practical problems where these basic assumptions are not met? If so, is the theory valid for any parent population, regardless of the shape of its distribution, and for extreme departures from the condition that the variables are independently distributed? These questions and others concerning problems arising in practice which may affect the applicability of the theory are discussed in this thesis. Abstracts of nine selected papers oon experimental sampling distributions are given in Chapter V. For the purpose of illustrating, applications of distribution theory are made under various conditions in the hope that the theory itself may be better understood. The experiments, as well as the thesis in general, pertain to four sampling distributions, namely; the normal, Chi-square, "F," and "t" distributions. In connection with the problem of showing the applicability of limiting (and other theoretical) distributions, the approach to normality is discussed for a number of statistics such as the mean and the correlation coefficient.